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Research Output 2003 2019

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2019
15 Downloads (Pure)

A regularised Dean-Kawasaki model: derivation and analysis

Cornalba, F., Shardlow, T. & Zimmer, J., 9 Apr 2019, In : Siam Journal on Mathematical Analysis. 51, 2, p. 1137-1187 51 p.

Research output: Contribution to journalArticle

Open Access
File

Harnessing fluctuations to discover dissipative evolution equations

Li, X., Dirr, N., Embacher, P., Zimmer, J. & Reina, C., 18 Jun 2019, In : Journal of the Mechanics and Physics of Solids. p. 240-251

Research output: Contribution to journalArticle

2018
2 Citations (Scopus)

Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

Kaiser, M., Jack, R. & Zimmer, J., 1 Mar 2018, In : Journal of Statistical Physics. 170, 6, p. 1019-1050

Research output: Contribution to journalArticle

Open Access
Fluctuations (theory)
Rate Function
Markov chains
orthogonality
Orthogonality
2 Citations (Scopus)

Computing diffusivities from particle models out of equilibrium

Embacher, P., Dirr, N., Zimmer, J. & Reina, C., 11 Apr 2018, In : Proceedings of the Royal Society of Edinburgh Section A - Mathematics. 474, 2212, p. 20170694 20170694.

Research output: Contribution to journalArticle

Open Access
Particle System
Diffusivity
Zero-range Process
Fluctuations
Exclusion Process

Effective Hamiltonian Dynamics via the Maupertuis Principle

Schwetlick, H., Sutton, D. & Zimmer, J., 31 Jul 2018, (Accepted/In press) In : Discrete and Continuous Dynamical Systems Series S.

Research output: Contribution to journalArticle

1 Citation (Scopus)
16 Downloads (Pure)

The semi-infinite asymmetric exclusion process: Large deviations via matrix products

Gonzalez Duhart Muñoz De Cote, H., Morters, P. & Zimmer, J., 1 Apr 2018, In : Potential Analysis. 48, 3, p. 301-323

Research output: Contribution to journalArticle

Open Access
File
Asymmetric Exclusion Process
Matrix Product
Large Deviations
Stationary Measure
Product Measure
1 Citation (Scopus)
24 Downloads (Pure)

Travelling wavefronts in nonlocal diffusion equations with nonlocal delay effects

Guo, S. & Zimmer, J., 1 Apr 2018, In : Bulletin of the Malaysian Mathematical Sciences Society. 41, 2, p. 919-943 25 p.

Research output: Contribution to journalArticle

Open Access
File
Nonlocal Delay
Nonlocal Diffusion
Traveling Wavefronts
Nonlocal Equations
Diffusion equation
2017
9 Citations (Scopus)
31 Downloads (Pure)
Open Access
File
Acceleration of Convergence
Convergence to Equilibrium
Hydrodynamic Limit
Detailed Balance
Markov chains
25 Downloads (Pure)

A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel

Zimmer, J., Patacchini, F., Hömberg, D. & Sakamoto, K., 1 Aug 2017, In : IMA Journal of Applied Mathematics. 82, 4, p. 763-780

Research output: Contribution to journalArticle

Open Access
File
Grain Size
Ferrite
Steel
Crystal microstructure
Identification (control systems)

Hydrodynamic limit of condensing two-species zero range processes with sub-critical initial profiles

Zimmer, J., Dirr, N. & Stamatakis, M., Aug 2017, In : Journal of Statistical Physics. 168, 4, p. 794–825

Research output: Contribution to journalArticle

Open Access
Zero-range Process
Hydrodynamic Limit
condensing
hydrodynamic equations
hydrodynamics
2 Citations (Scopus)
24 Downloads (Pure)

Symmetries and Geometrical Properties of Dynamical Fluctuations in Molecular Dynamics

Jack, R., Kaiser, M. & Zimmer, J., 22 Oct 2017, In : Entropy. 19, 10, p. 562 - 562 1 p.

Research output: Contribution to journalArticle

Open Access
File
molecular dynamics
symmetry
nonconservative forces
deviation
heat transmission
2 Citations (Scopus)
45 Downloads (Pure)

Travelling waves for a Frenkel-Kontorova chain

Buffoni, B., Zimmer, J. & Schwetlick, H., 15 Aug 2017, In : Journal of Differential Equations. 263, 4, p. 2317-2342

Research output: Contribution to journalArticle

Open Access
File
Traveling Wave
Dislocation Dynamics
Frenkel-Kontorova Model
Arc of a curve
Fixed point
2016
4 Citations (Scopus)
118 Downloads (Pure)

Entropic and gradient flow formulations for nonlinear diffusion

Dirr, N., Stamatakis, M. & Zimmer, J., 1 Aug 2016, In : Journal of Mathematical Physics. 57, 8, 081505.

Research output: Contribution to journalArticle

Open Access
File
Gradient Flow
Nonlinear Diffusion
Thermodynamics
Zero-range Process
formulations
2015
6 Citations (Scopus)
83 Downloads (Pure)

Entropy production and the geometry of dissipative evolution equations

Zimmer, J. & Reina, C., 13 Nov 2015, In : Physical Review E (PRE). 92, 5, 052117.

Research output: Contribution to journalArticle

Open Access
File
46 Downloads (Pure)

On the Γ-limit for a non-uniformly bounded sequence of two-phase metric functionals

Schwetlick, H., Sutton, D. C. & Zimmer, J., Jan 2015, In : Discrete and Continuous Dynamical Systems - Series A. 35, 1, p. 411-426 16 p.

Research output: Contribution to journalArticle

File
Hamiltonians
Nonlinear optics
Boundary value problems
Metric
Differentiable Manifolds
14 Citations (Scopus)

Stability of travelling wavefronts in discrete reaction-diffusion equations with nonlocal delay effects

Guo, S. & Zimmer, J., Feb 2015, In : Nonlinearity. 28, 2, p. 463-492 30 p.

Research output: Contribution to journalArticle

Nonlocal Delay
Traveling Wavefronts
reaction-diffusion equations
energy methods
Discrete Equations
2014
10 Citations (Scopus)
43 Downloads (Pure)

Conservative-dissipative approximation schemes for a generalized Kramers equation

Duong, M. H., Peletier, M. A. & Zimmer, J., 15 Nov 2014, In : Mathematical Methods in the Applied Sciences. 37, 16, p. 2517-2540 24 p.

Research output: Contribution to journalArticle

File
Approximation Scheme
Generalized Equation
Stochastic systems
Dissipative Structure
Costs
8 Citations (Scopus)
45 Downloads (Pure)

Geometrical interpretation of fluctuating hydrodynamics in diffusive systems

Jack, R. L. & Zimmer, J., 5 Dec 2014, In : Journal of Physics A: Mathematical and Theoretical. 47, 48, 485001.

Research output: Contribution to journalArticle

File
Fluctuating Hydrodynamics
Hydrodynamics
hydrodynamics
Mesoscopic Systems
formulations
1 Citation (Scopus)
56 Downloads (Pure)

Travelling lattice waves in a toy model of Lennard-Jones interaction

Venney, C. R. & Zimmer, J., 1 Mar 2014, In : Quarterly of Applied Mathematics. 72, 1, p. 65-84 20 p.

Research output: Contribution to journalArticle

Open Access
File
Lennard-Jones potential
Lennard-Jones
Nearest Neighbor
Interaction
Periodic Solution
2013
4 Citations (Scopus)

Can equations of equilibrium predict all physical equilibria? A case study from Field Dislocation Mechanics

Das, A., Acharya, A., Zimmer, J. & Matthies, K., Nov 2013, In : Mathematics and Mechanics of Solids. 18, 8, p. 803-822 20 p.

Research output: Contribution to journalArticle

Dislocation
Mechanics
Ginzburg-Landau Equation
Predict
Microstructure
30 Citations (Scopus)
56 Downloads (Pure)

GENERIC formalism of a Vlasov-Fokker-Planck equation and connection to large-deviation principles

Duong, M. H., Peletier, M. A. & Zimmer, J., Nov 2013, In : Nonlinearity. 26, 11, p. 2951-2971 21 p.

Research output: Contribution to journalArticle

Open Access
File
Fokker Planck equation
Vlasov Equation
Large Deviation Principle
Particle System
Variational Formulation
21 Citations (Scopus)
56 Downloads (Pure)

Large deviations and gradient flows

Adams, S., Dirr, N., Peletier, M. & Zimmer, J., 28 Dec 2013, In : Philosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences. 371, 2005, 0341.

Research output: Contribution to journalArticle

File
Gradient Flow
Large Deviation Principle
Brownian movement
Large Deviations
Free energy
6 Citations (Scopus)
68 Downloads (Pure)

Subsonic phase transition waves in bistable lattice models with small spinodal region

Herrmann, M., Matthies, K., Schwetlick, H. & Zimmer, J., 3 Sep 2013, In : SIAM Journal on Mathematical Analysis (SIMA). 45, 5, p. 2625-2645 21 p.

Research output: Contribution to journalArticle

Open Access
File
Lattice Model
Phase Transition
Phase transitions
Perturbation
Kinetic Relation
2012
5 Citations (Scopus)
58 Downloads (Pure)

Kinetic relations for a lattice model of phase transitions

Schwetlick, H. & Zimmer, J., 1 Nov 2012, In : Archive for Rational Mechanics and Analysis. 206, 2, p. 707-724 18 p.

Research output: Contribution to journalArticle

Open Access
File
Kinetic Relation
Lattice Model
Traveling Wave Solutions
Phase Transition
Phase transitions
1 Citation (Scopus)
55 Downloads (Pure)

Nonexistence of slow heteroclinic travelling waves for a bistable Hamiltonian lattice model

Schwetlick, H., Sutton, D. C. & Zimmer, J., Dec 2012, In : Journal of Nonlinear Science. 22, 6, p. 917-934 18 p.

Research output: Contribution to journalArticle

Open Access
File
Hamiltonians
Lattice Model
Traveling Wave
Nonexistence
Corrector
2 Citations (Scopus)
67 Downloads (Pure)

On selection criteria for problems with moving inhomogeneities

Herrmann, M., Schwetlick, H. & Zimmer, J., 1 Jan 2012, In : Continuum Mechanics and Thermodynamics. 24, 1, p. 21-36 16 p.

Research output: Contribution to journalArticle

File
inhomogeneity
Thermodynamics
Fluxes
thermodynamics
energy
1 Citation (Scopus)
43 Downloads (Pure)

Rate-independent processes with linear growth energies and time-dependent boundary conditions

Kruzik, M. & Zimmer, J., Jun 2012, In : Discrete and Continuous Dynamical Systems Series S. 5, 3, p. 591-604 14 p.

Research output: Contribution to journalArticle

File
Rate-independent Processes
Energy Density
Infinity
Boundary conditions
Evolution Problems
9 Citations (Scopus)
58 Downloads (Pure)

Upscaling from particle models to entropic gradient flows

Dirr, N., Laschos, V. & Zimmer, J., 2012, In : Journal of Mathematical Physics. 53, 6, 063704.

Research output: Contribution to journalArticle

Open Access
File
Upscaling
Gradient Flow
Asymptotically equivalent
Time Discretization
Real Line
2011
9 Citations (Scopus)

A model of shape memory alloys taking into account plasticity

Kruizik, M. & Zimmer, J., Feb 2011, In : IMA Journal of Applied Mathematics. 76, 1, p. 193-216 24 p.

Research output: Contribution to journalArticle

Shape Memory
Shape memory effect
Plasticity
Dissipation
Plastics
4 Citations (Scopus)
58 Downloads (Pure)

Existence of subsonic heteroclinic waves for the Frenkel-Kontorova model with piecewise quadratic on-site potential

Kreiner, C. F. & Zimmer, J., Apr 2011, In : Nonlinearity. 24, 4, p. 1137-1163 27 p.

Research output: Contribution to journalArticle

Open Access
File
Dislocation Dynamics
Frenkel-Kontorova Model
traveling waves
Traveling Wave
Framework
40 Citations (Scopus)
55 Downloads (Pure)

From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage

Adams, S., Dirr, N., Peletier, M. & Zimmer, J., 1 Nov 2011, In : Communications in Mathematical Physics. 307, 3, p. 791-815 25 p.

Research output: Contribution to journalArticle

Open Access
File
Gradient Flow
Large Deviation Principle
Diffusion equation
Particle System
deviation
9 Citations (Scopus)
63 Downloads (Pure)

Mathematical concepts for the micromechanical modelling of dislocation dynamics with a phase-field approach

Kundin, J., Emmerich, H. & Zimmer, J., Jan 2011, In : Philosophical Magazine. 91, 1, p. 97-121 25 p.

Research output: Contribution to journalArticle

Open Access
File
materials science
microbalances
solidification
phase transformations
degrees of freedom
2 Citations (Scopus)
58 Downloads (Pure)
Open Access
File
Lennard-Jones potential
Persistence
Nearest Neighbor
Periodic Solution
Interaction
2010
32 Downloads (Pure)

A variational approach to the Hamiltonian boundary value problem: Existence and approximation

Zimmer, J. & Schwetlick, H., Mar 2010, In : Oberwolfach Reports. 7, 1, p. 792-794 3 p.

Research output: Contribution to journalArticle

File
4 Citations (Scopus)
45 Downloads (Pure)

Evolutionary problems in non-reflexive spaces

Kruzik, M. & Zimmer, J., Jan 2010, In : Esaim-Control Optimisation and Calculus of Variations. 16, 1, p. 1-22 22 p.

Research output: Contribution to journalArticle

File
Energy Density
Rate-independent Processes
Infinity
Homogeneous Function
Quasiconvex
14 Citations (Scopus)
58 Downloads (Pure)

Three-dimensional model of martensitic transformations with elasto-plastic effects

Kundin, J., Emmerich, H. & Zimmer, J., Apr 2010, In : Philosophical Magazine. 90, 11, p. 1495-1510 16 p.

Research output: Contribution to journalArticle

Open Access
File
martensitic transformation
three dimensional models
plastics
austenite
microstructure
10 Citations (Scopus)
62 Downloads (Pure)

Travelling wave solutions for a quasilinear model of field dislocation mechanics

Acharya, A., Matthies, K. & Zimmer, J., Dec 2010, In : Journal of the Mechanics and Physics of Solids. 58, 12, p. 2043-2053 11 p.

Research output: Contribution to journalArticle

File
traveling waves
drag coefficients
Drag coefficient
Mechanics
scalars
2009
54 Downloads (Pure)

Asymptotics of resonances in a thermoelastic model with light local mass perturbations

Babych, N. & Zimmer, J., Jun 2009, In : Quarterly of Applied Mathematics. 67, 2, p. 311-326 16 p.

Research output: Contribution to journalArticle

Open Access
File
8 Citations (Scopus)
31 Downloads (Pure)
File
Hamiltonians
Equations of motion
Mechanics
Trajectories
trajectories
20 Citations (Scopus)
55 Downloads (Pure)
File
6 Citations (Scopus)
55 Downloads (Pure)

Gradient flows in asymmetric metric spaces

Chenchiah, I. V., Rieger, M. O. & Zimmer, J., 2009, In : Nonlinear Analysis: Theory Methods & Applications. 71, 11, p. 5820-5834 15 p.

Research output: Contribution to journalArticle

Open Access
File
Gradient Flow
Metric space
Hysteresis
Topology
Mathematical models
4 Citations (Scopus)
43 Downloads (Pure)

Heteroclinic travelling waves for the lattice sine-Gordon equation with linear pair interaction

Kreiner, C. F. & Zimmer, J., Nov 2009, In : Discrete and Continuous Dynamical Systems. 25, 3, p. 915-931 17 p.

Research output: Contribution to journalArticle

File
sine-Gordon equation
Concentration-compactness
Sine-Gordon Equation
Traveling Wave
Atoms
1 Citation (Scopus)
58 Downloads (Pure)

Modeling transformation paths of multiphase materials: The triple point of zirconia

Dondl, P. W., Hormann, K. & Zimmer, J., Mar 2009, In : Physical Review B. 79, 10, 104114.

Research output: Contribution to journalArticle

File
zirconium oxides
Zirconia
modulus of elasticity
Elastic moduli
three dimensional models

On an extension of the space of bounded deformations

Kruzik, M. & Zimmer, J., 2009, In : Zeitschrift für Analysis und ihre Anwendungen. 31, 1, p. 75-91 17 p.

Research output: Contribution to journalArticle

8 Citations (Scopus)
59 Downloads (Pure)

Travelling wave solutions for the discrete sine-Gordon equation with nonlinear pair interaction

Kreiner, C. F. & Zimmer, J., 2009, In : Nonlinear Analysis: Theory Methods & Applications. 70, 9, p. 3146-3158 13 p.

Research output: Contribution to journalArticle

Open Access
File
sine-Gordon equation
Concentration-compactness
Mountain Pass
Periodic Wave
Sine-Gordon Equation
3 Citations (Scopus)
60 Downloads (Pure)

Young measure flow as a model for damage

Rieger, M. O. & Zimmer, J., Jan 2009, In : Zeitschrift für Angewandte Mathematik und Physik. 60, 1, p. 1-32 32 p.

Research output: Contribution to journalArticle

File
Quasistatic Evolution
Global Minimization
Variational Model
Young Measures
Gradient Flow
2008
39 Downloads (Pure)

Travelling waves in atomistic chains and kinetic relations

Zimmer, J., 2008, In : Oberwolfach Reports. 5, 2, p. 1079-1156

Research output: Contribution to journalArticle

File
2007
20 Citations (Scopus)
51 Downloads (Pure)

An asymmetric Arzela-Ascoli theorem

Collins, J. & Zimmer, J., 1 Jun 2007, In : Topology and Its Applications. 154, 11, p. 2312-2322 11 p.

Research output: Contribution to journalArticle

File
Arzela-Ascoli Theorem
Quasi-metric Space
Metric space
15 Downloads (Pure)

Discrete dynamic models for phase transitions

Zimmer, J. & Schwetlick, H., 2007, In : Oberwolfach Reports.

Research output: Contribution to journalArticle

File